Factual error: When Conan cuts off Thulsa Doom's head, and throws it over the parapet, it hits the stairs below and rolls a little way down. Not only are there absolutely no marks left on the stairs (there should at least be a small amount of blood), it sounds like something plastic is rolling down there.
STP
Answer: Like an Army Drill Sargent, he was berating them for not doing it better. Toughening them to become the best they could be.
Also, the other student laughs at Conan's punishment, so the teacher kicks him to teach him some humility.